A force-directed graph (using *arbor.js*) showing the orbits of small numbers under the Collatz map. Lothar Collatz first proposed the following conjecture in 1937: Take any natural number $n$. If $n$ is even, divide it by 2 to get $n / 2$. If $n$ is odd, multiply it by 3 and add 1 to obtain $3n + 1$. Repeat the process indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. In 1972, J. H. Conway proved that a natural generalization of the Collatz problem is algorithmically undecidable.